J. Hong

Nan Jiang, Jiadong Hong, Lei Liu et al.

Learning-based MIMO detection has shown strong empirical performance, yet existing methods typically rely on fixed-depth architectures without explicitly modeling the progressive refinement of symbol estimates. In this paper, we revisit MIMO detection from a flow matching perspective and propose the Soft Graph Diffusion Transformer (SGDiT), which reformulates detection as a noise-level-conditioned denoising process that progressively transforms a Gaussian initialization toward the posterior conditioned on channel observations. An adaptive layer normalization (AdaLN)-conditioned soft graph transformer is employed to parameterize the denoising dynamics, enabling stage-aware information integration between observation and symbol domains. To better align with the discrete nature of symbol detection, we further adopt a cross-entropy-based training objective that directly models bit-wise posterior probabilities, providing a more suitable inductive bias than conventional regression-based formulations. Experimental results across various MIMO system configurations demonstrate that SGDiT achieves competitive bit error rate (BER) performance compared with representative baselines. Furthermore, the proposed model exhibits good generalization capability across different channel conditions. Overall, the SGDiT framework provides an effective and practical approach for neural MIMO detection.

Jiadong Hong, Lei Liu, Xinyu Bian et al.

Flow matching has emerged as a powerful framework for generative modeling, with recent empirical successes highlighting the effectiveness of signal-space prediction ($x$-prediction). In this work, we investigate the transfer of this paradigm to binary manifolds, a fundamental setting for generative modeling of discrete data. While $x$-prediction remains effective, we identify a latent structural mismatch that arises when it is coupled with velocity-based objectives ($v$-loss), leading to a time-dependent singular weighting that amplifies gradient sensitivity to approximation errors. Motivated by this observation, we formalize prediction-loss alignment as a necessary condition for flow matching training. We prove that re-aligning the objective to the signal space ($x$-loss) eliminates the singular weighting, yielding uniformly bounded gradients and enabling robust training under uniform timestep sampling without reliance on heuristic schedules. Finally, with alignment secured, we examine design choices specific to binary data, revealing a topology-dependent distinction between probabilistic objectives (e.g., cross-entropy) and geometric losses (e.g., mean squared error). Together, these results provide theoretical foundations and practical guidelines for robust flow matching on binary -- and related discrete -- domains, positioning signal-space alignment as a key principle for robust diffusion learning.